Examination of a discrete stochastic epidemic model with high risk and quarantine classes

Abstract

We propose a new discrete-time stochastic epidemic compartment model to study and analyze the spread of disease. The SRhQIHR model consists of six compartments; Susceptible (S), High risk (Rh), Quarantined (Q), Infected (I), Hospitalized (H) and Co-advisor Co-advisor Recovered (R). The high risk class (Rh) comprises individuals who are at higher risk of infection compared to the general susceptible population, such as those with close contact to infected individuals. Transitions between compartments are assumed to follow certain probability distributions that capture the movement of individuals. The advancement of tracking technologies enables the differentiation of high risk individuals from susceptible ones through the use of tracking equipment or mobile applications. Therefore, this model f inds relevance in technology-ready societies. We utilize the SRhQIHR model to forecast the future spread of diseases. The model incorporates both the transmission dynamics of epidemics and measures to control their spread. We examine the mathematical analysis of the model such as long-term behavior, the basic reproduction number and sensitivity analysis. Moreover, the Monte Carlo simulation can be employed to study the survival distribution of the outbreak, the final size of infected individuals, and the expected duration of the epidemic. By this comprehensive approach, our model provides valuable insights for understanding and managing disease outbreaks in various scenarios. Additionally, we present the optimal control techniques applied to the SRhQIHR model by considering two control strategies, namely, the quarantine and isolation strategies.